924/MR00. problem / Math - Solved Math Problems

MR-924. problem

Determine the length of the segment FE if AB=5cm, CD=3cm, AF=10cm!

$∆ A B C ~ ∆ E F C$

$\frac{5}{10 + y} = \frac{x}{y}$

$∆ A C D ~ ∆ A E F$

$\frac{3}{10 + y} = \frac{x}{10}$

$10 + y = \frac{5 y}{x}$

$10 + y = \frac{30}{x}$

$\frac{5 y}{x} = \frac{30}{x}$

$5 y = 30$

$y = \frac{30}{5}$

$y = 6$

$\frac{5}{10 + y} = \frac{x}{y}$

$\frac{5}{10 + 6} = \frac{x}{6}$

$x = \frac{5 \cdot 6}{10 + 6}$

$x = \frac{30}{16}$

$\bar{F E} = x = \frac{15}{8}$

MathReference - Problems